$ψ$DAG: Projected Stochastic Approximation Iteration for DAG Structure Learning

Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined this problem as a continuous optimization task by incorporating differentiable acyclicity constraints. These methods commonly rely on algebraic characterizations of DAGs, such as matrix exponentials, to enable the use of gradient-based optimization techniques. Despite these innovations, existing methods often face optimization difficulties due to the highly non-convex nature of DAG constraints and the per-iteration computational complexity. In this work, we present a novel framework for learning DAGs, employing a Stochastic Approximation approach integrated with Stochastic Gradient Descent (SGD)-based optimization techniques. Our framework introduces new projection methods tailored to efficiently enforce DAG constraints, ensuring that the algorithm converges to a feasible local minimum. With its low iteration complexity, the proposed method is well-suited for handling large-scale problems with improved computational efficiency. We demonstrate the effectiveness and scalability of our framework through comprehensive experimental evaluations, which confirm its superior performance across various settings.

MirrorCheck: Efficient Adversarial Defense for Vision-Language Models

Vision-Language Models (VLMs) are becoming increasingly vulnerable to adversarial attacks as various novel attack strategies are being proposed against these models. While existing defenses excel in unimodal contexts, they currently fall short in safeguarding VLMs against adversarial threats. To mitigate this vulnerability, we propose a novel, yet elegantly simple approach for detecting adversarial samples in VLMs. Our method leverages Text-to-Image (T2I) models to generate images based on captions produced by target VLMs. Subsequently, we calculate the similarities of the embeddings of both input and generated images in the feature space to identify adversarial samples. Empirical evaluations conducted on different datasets validate the efficacy of our approach, outperforming baseline methods adapted from image classification domains. Furthermore, we extend our methodology to classification tasks, showcasing its adaptability and model-agnostic nature. Theoretical analyses and empirical findings also show the resilience of our approach against adaptive attacks, positioning it as an excellent defense mechanism for real-world deployment against adversarial threats.